Chapter - 3

Resistances in parallel: The combine resistance of a number of resistances connected in parallel can be calculated by using the law of combination of resistances in parallel. According to this law : the reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.

If a number of resistances R1, R2, R3..... etc are connected in paralle then the total resistance R of the combination is given by the formula
                      1/ R = 1/ R1 + 1/R2 + 1/R3.......

Note: when a number of resistances are connected in parallel then their combined resistance is less than the smallest individual resistance.

Before we drive a formula for the resistance of a number of resistances connected in parallel, we should keep in mind that:

  1. When a number of resistances are connected in parallel, then the potential difference across each resistance is the same which is equal to the voltage of the battery applied.
  2. When a  number of resistances connected in parallel are joined to the terminals of battery, then different amount of current flow through each resistance, but the current flowing through all the individual parallel resistances, taken together, is equal to the current flowing in the circuit as a whole. Thus, when a  number of resistances are connected in parallel, then  the sum of the currents flowing through all the resistances is equal to the total current flowing in the circuit.

Combine resistance of two resistances connected in parallel: If two resistances R1 and R2 are connected in parallel to one another b/w the same point A and B. A battery of V volts has been applied across the ends of this combination. In this case the potential difference across the ends of the both resistances will be the same. And it will be the equal to the voltage of the battery used. The current flowing through the two resistances in parallel is, however not the same
Suppose the total current flowing in the circuit is I, then the current passing through R1 is I1 and R2 is I2 respectively. Then total current in the circuit
                               I = I1 + I2 .....................(i)

We know by ohm’s law    I = V/R then
              Since the potential V across both the resistance R1 and R2 in parallel is the same, so by applying ohm’s law to each resistance separately we get
                             I1 = V / R1 and I2 = V / R2 

Now putting teh values if I1 and I2 in equation (i)
                         V/R = V / R1+ V / R2     and we get
                       1/ R = 1/R1 + 1/ R2

Domestic electric circuits: series or parallel : When designing an electric circuit, we should consider whether a series or parallel circuit is better for the intended use: for example, if we want to connect a large number of electric bulbs for decorating buildings and trees as during festivals such as Diwali or marriage function, then the series circuit is better because all bulbs connected in series can be controlled with just one switch. A series circuit is also safer because the current in it smaller. But there is a problem with this circuit. This is because if one bulb gets fused, then the circuit breaks and all the bulbs are turned off. An electrician has to spend a lot of time in locating the fused bulb form among hundreds bulbs, so as to replace it and restore the lighting.
      

  The parallel electric circuit is better for connecting bulbs in house because then we can have separate switches for each bulb and hence operate it separately. In addition to having ease of operation, parallel domestic circuits have many other advantages over the series circuits. 

Disadvantages of series circuit s for domestic wiring:
       There are some following disadvantages of series circuits in the domestic wiring:

  1. In series circuit, if one electrical appliance stops working due to some defect, then all other appliances also stop working.
  2. In series, all the electrical appliances have only one switch due to which they can’t be turn off or on separately.
  3. In series circuit, the appliances do not get the same voltage as that of the power supply line.
  4. In the series connection of electrical appliance, the overall resistance of the circuit increases too much due to  which the current from the power supply is low.

Advantages of parallel circuits in domestic wring:
         There are some following advantages of parallel circuits in the domestic wiring:

  1. In parallel circuits, if one electrical appliance stop working due to some effect then all other appliances keep working normally.
  2. In parallel circuit, each electrical appliance has own switch due to which it can be turn off or on independently, without effecting  other appliances.
  3. In parallel circuits, each electrical appliance gets same voltage as that of the power supply line.
  4. In the parallel connection of electrical appliances, the overall resistance of the house hold circuit is reduced due to which the current from the power supply is high.

Electric power:
 we know that the rate of doing work is known as power, so electric power is the electrical work done per unit. That is
                                    Power = work done / time taken
                                    Or              P = W/ t

Unit of power: The s.i. unit of electric power is watt denoted by the letter W, the power of 1 watt is a rate of working of 1 joule per second. That is
                                      1 Watt = 1 joule / 1 second
         

          Watt is a small unit, therefore, a bigger unit of electric power called kilowatt is used for commercial purpose. That is
                                        One kilo watt = 1000 watts
                                        1 kW = 1000 watts or 103 watts 

So we can say that electric power is the rate at which electrical energy is consumed or electric ower is the electrical energy consumed per second.
We can write down the another definition of electric power, when electric appliance is consumes electrical energy at the rate of 1 joule per second, its power is said to be 1 watt.
We know that
                                Power = work done / time taken
Or                                  p = W /t    ---------------------(i)

But we know that the work done W by current I when it flows for time t under a potential difference V is given by
                              W = V x I  x t

Put this value in equation (i), we get
                          P = (V x I x t)/ t
                          P = V X I watts

Where, V = potential difference and I = current in amperes
                    Electric power = potential difference X current 

 

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